Spin foam models of quantum gravity: spacetime as a discrete 2-complex. Each face carries spin j (area eigenvalue A=8πℓ_P²γ√(j(j+1))). The Ponzano-Regge amplitude is a product of {6j}-symbols. Discrete area spectrum is a prediction of LQG.
Area eigenvalues (in ℓ_P² units):
Total area: — ℓ_P²
Ponzano-Regge amplitude:
A ~ Σ_{j_f} Π_f (2j_f+1) Π_v {6j}
Saddle point j→∞:
A → e^{iS_Regge[g]} (classical GR!)
{6j} symbol = Wigner 6j
j→∞: {6j}≈cos(S_tet+π/4)/√V_tet
Discrete area spectrum A=8πγℓ_P²√(j(j+1)) — no continuum!